Definition 70.18.1. With $Z \subset B$ and $f : X \to B$ as above.

1. Given a quasi-coherent $\mathcal{O}_ X$-module $\mathcal{F}$ the strict transform of $\mathcal{F}$ with respect to the blowup of $B$ in $Z$ is the quotient $\mathcal{F}'$ of $\text{pr}_ X^*\mathcal{F}$ by the submodule of sections supported on $|\text{pr}_{B'}^{-1}E|$.

2. The strict transform of $X$ is the closed subspace $X' \subset X \times _ B B'$ cut out by the quasi-coherent ideal of sections of $\mathcal{O}_{X \times _ B B'}$ supported on $|\text{pr}_{B'}^{-1}E|$.

There are also:

• 2 comment(s) on Section 70.18: Strict transform

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).